What is the target Q-value in DQNs?
When training a Deep Q network with experienced replay, you accumulate what is known as training experiences $e_t = (s_t, a_t, r_t, s_{t+1})$. You then sample a batch of such experiences and for each sample you do the following.


Feed $s_t$ into the network to get $Q(s,a;\theta)$.
Feed $s_{t+1}$ into the network to get $Q(s’,a’,\theta)$.
Choose $max_aQ(s’,a’,\theta)$ and set $ \gamma max_aQ(s’,a’,θ)$ + $r_t$ as the target of the network.
Train the network with $s_t$ as input to update $\theta$. The output from the input of $s_t$ is $Q(s,a,\theta)$ and the gradient descent step minimises the squared distance between $Q(s,a,\theta)$ and $\gamma max_aQ(s’,a’,θ)$ + $r_t$